Is it possible to render frames out of order?
I would do this via scripting.  Here I modified an existing script that would do your remapping of frame# into file index#.  You would adjust firstBreak to 60 and lastFrame to 168.
import bpy

filepathFmt=&quot;//render/frame {0:04d}.png&quot;

firstBreak=8
lastFrame=11

###
### for list of shape types, N loops, create a set of objects, render and save, and clean up:
###
fp=&quot;&quot;
outFileIdx=1

### render from firstBreak to lastFrame:
for frameIdx in range(firstBreak, lastFrame+1, 1):
    
    bpy.context.scene.frame_set(frame=frameIdx)
    print(&quot;frame=&quot; + str(frameIdx))
    # format filename string using different index
    fp = filepathFmt.format( outFileIdx )
    print(outFileIdx)
    print( fp )
    bpy.context.scene.render.filepath = fp
    bpy.ops.render.render( write_still=True )
    outFileIdx+=1

print(&quot;remap&quot;)

### render from frame 1 to firstBreak-1:
for frameIdx in range(1, firstBreak, 1):
    
    bpy.context.scene.frame_set(frame=frameIdx)
    print(&quot;frame=&quot; + str(frameIdx))
        
    ### render and save:
    # format filename string using different index
    fp = filepathFmt.format( outFileIdx )
    print(outFileIdx)
    print( fp )
    bpy.context.scene.render.filepath = fp
    bpy.ops.render.render( write_still=True )
    outFileIdx+=1
```